2016 Spring

2015 Fall

I will talk about large deviation theory and its applications. For the first talk, my plan is to introduce Gartner-Ellis theorem and show a few applications of it to finite state discrete time Markov chains.

9/29, 10/6, 10/13 :Dae Han

10/20, 10/27, 11/3: Jessica

I will first present an overview of concentration of measure and concentration inequalities with a focus on the connection with related topics in analysis and geometry. Then, I will present Log-Sobolev inequalities and their connection to concentration of measure.

11/10, 11/17: Hao Kai

11/24, 12/1, 12/8, 12/15: Chris

2016 Spring:

2/2, 2/9: Louis

2/16, 2/23: Jinsu

3/1, 3/8: Hans

2015 Spring

2/3, 2/10: Scott

An Introduction to Entropy for Random Variables

In these lectures I will introduce entropy for random variables and present some simple, finite state-space, examples to gain some intuition. We will prove the
MacMillan Theorem using entropy and the law of large numbers. Then I will introduce relative entropy and prove the Markov Chain Convergence Theorem. Finally I will
define entropy for a discrete time process. The lecture notes can be found at http://www.math.wisc.edu/~shottovy/EntropyLecture.pdf.

2/17, 2/24: Dae Han

3/3, 3/10: Hans

3/17, 3/24: In Gun

4/7, 4/14: Jinsu

4/21, 4/28: Chris N.

2014 Fall

9/23: Dave

I will go over Mike Giles’ 2008 paper “Multi-level Monte Carlo path simulation.” This paper introduced a new Monte Carlo method to approximate expectations of SDEs (driven by Brownian motions) that is significantly more efficient than what was the state of the art. This work opened up a whole new field in the numerical analysis of stochastic processes as the basic idea is quite flexible and has found a variety of applications including SDEs driven by Brownian motions, Levy-driven SDEs, SPDEs, and models from biology

9/30: Benedek

A very quick introduction to Stein's method.

I will give a brief introduction to Stein's method, mostly based on the the first couple of sections of the following survey article: